a term, generally used perjoratived or critically (like 'NIMBY' itself), meaning behavior or statements that match NIMBY patterns and are from 'left' or progressive identified parties. Earliest usage found is 2013: 
 

a 2013 comment on a story at Lawyers, Guns, & Money blog about Seattle politics and Councilmember Kshama Sawant: 

"I also find Left NIMBYism a bit more annoying than Right NIMBYism because Right NIMBYs are bit more honest with their goals of wanting to keep things the same, keep the wrong sort of people out, etc. Left NIMBYism likes to present itself as populist in spirit but a lot of its based on falsely romantic notions about keeping the neighborhood the same as it was when you were young and just moved in."

 

Benjamin Ross [2014]. Dead End: Suburban Sprawl and the Rebirth of American Urbanism, "left+NIMBYism"&source=bl&ots=5zkDtSocvU&sig=cfndloTh28N_pkeKO7hjucNPoCs&hl=en&sa=X&ved=2ahUKEwiDxtHN6p_eAhUxPn0KHR2HB94Q6AEwA3oECAMQAQ#v=onepage&q="left%20NIMBYism"&f=false passage on p.99

"The evolution of left nimbyism is exemplified by Zelda Bronstein, a socialist feminist historian who chaired the Berkeley Planning Commission from 2002 to 2004."

 

Roderick M Hills, Jr. [2018]. "Why do so many affordable-housing advocates reject the law of supply and demand?The Washington Post, Sept 18, 2018: 

"YIMBYs face enormous opposition from self-styled progressives who flatly dismiss the idea that adding new market-rate housing to a city will improve housing affordability. Sometimes these activists go even further and argue that adding market-rate housing to cities actively hurts the poor (on the grounds that expensive apartments attract wealthier residents who bid up rents). Such activists will fiercely oppose even new market-rate buildings that include subsidized units.

"They end up allying themselves with NIMBY (“Not in My Back Yard”) homeowners who oppose all new construction in their neighborhoods. Working together, the two groups help choke off new construction that could ease housing prices.

"Call this attitude “Left NIMBYism.” Left NIMBYism not only flatly contradicts the logic of supply and demand but also flies in the face of empirical studies of what happens when cities see new construction. In its stubborn rejection of empirical reality, the Left NIMBYist view of housing markets shares characteristics of ideologically motivated refusals to accept evidence in other contexts, such as climate change or the safety of vaccines."

 

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